In recent years, there have been numerous theoretical innovations and prototype testing efforts that have demonstrated the advantages of Reconfigurable Intelligent Surfaces (RIS) technology in terms of low cost, low power, and ease of deployment, as well as numerous potential opportunities and broad application prospects for future 6G networks. However, implementing beamforming with RIS can be challenging, especially in the case of beam widening requirements. This paper proposes a dedicated Genetic Algorithms (GA)based algorithm for beamwidening in RIS-based communications. The main idea of this paper, with respect to previous studies published in the literature is that it ensures an enhanced control of wide beam characteristics by adjusting the constraints of the cost function optimized by GA.